LHC Physics Potential Vs. Energy: Considerations for the 2011 Run Chris Quigg*

FERMILAB–FN–0913–T Rev. February 1, 2011

LHC Physics Potential vs. Energy: Considerations for the 2011 Run Chris Quigg*

Theoretical Physics Department Fermi National Accelerator Laboratory Batavia, Illinois 60510 USA and CERN, Department of Physics, Theory Unit CH1211 Geneva 23, Switzerland

Parton luminosities are convenient for estimating how the physics potential of Large Hadron Collider experiments depends on the energy of the proton beams. I quantify the advantage of increasing the beam energy from 3.5 TeV to 4 TeV. I present parton luminosities, ratios of parton luminosities, and contours of fixed parton luminosity for gg, ud¯, qq, and gq interactions over the energy range relevant to the Large Hadron Collider, along with arXiv:1101.3201v2 [hep-ph] 1 Feb 2011 example analyses for specific processes. This note ex- tends the analysis presented in Ref. [1]. Full-size figures are available as pdf files at lutece.fnal.gov/PartonLum11/.

*E-mail:[email protected] 2 Chris Quigg

1 Preliminaries

The 2009-2010 run of the Large Hadron Collider at CERN is complete, with the delivery of some 45 pb−1 of proton-proton collisions at 3.5 TeV per beam to the ATLAS and CMS experiments. The primary objective of the run, to commission and ensure stable operation of the accelerator complex and the experiments, has been achieved, and much has been learned about machine operation. The experiments succeeded in “rediscovering” the standard model of particle physics, and using familiar physics objects such as W ±, Z0, J/ψ, Υ, jets, b-hadrons, and top-quark pairs to tune detector performance. In a few cases, LHC experiments have begun to explore virgin territory and surpass the discovery reach of the Tevatron experiments CDF and D0 [2].

Coming soon is an extended physics run during 2011-2012, with the goal of logging 1 fb−1 by the end of 2011 and perhaps 5 fb−1 by the end of 2012. Still to be decided is whether to raise the proton energy from 3.5 TeV to 4 TeV per beam. The object of this note√ is to quantify the enhanced√ sensitivity that would follow from running at s = 8 TeV rather than s = 7 TeV by considering some key parton luminosities. The choice of energy impacts the comparison of sensitivities at the LHC and the Tevatron. Taking the long view, it is also important to keep in√ mind how much is to be gained by approaching the LHC design energy of s = 14 TeV.

Detailed simulations of signals and backgrounds are of unquestioned value for in-depth consideration of the physics possibilities, especially in view of experience gained during the 2009-2010 run of the LHC. Higher-order perturbative-QCD calculations add insight [3]. However, much can be learned about the general issues of energy, luminosity, and the relative merits of proton-proton and proton-antiproton collisions√ by comparing the luminosities of parton-parton collisions as a function of sˆ, the c.m. energy of the colliding partons [4]. [A high-energy proton is, in essence, a broadband un- separated beam of quarks, antiquarks, and gluons.] By contemplating the parton luminosities in light of existing theoretical and experimental knowledge, physicists should be able to anticipate and critically examine the broad results of Monte Carlo studies. The more prior knowledge a user brings to the parton luminosities, the more useful insights they can reveal. LHC Physics Potential—2011 Run 3

Taking into account the 1/sˆ behavior of the hard-scattering processes that deﬁne much of the physics motivation for a multi-TeV hadron collider, the parton luminosity

Z 1 τ dLij τ/sˆ (a) (b) (a) (b) ≡ dx[fi (x)fj (τ/x) + fj (x)fi (τ/x)]/x, (1) sˆ dτ 1 + δij τ which has dimensions of a cross section, is a convenient measure of the reach (a) of a collider of given energy and hadron-hadron luminosity. Here fi (x) is the number distribution of partons of species i carrying√ momentum fraction x of hadron a. For hadrons colliding with c.m. energy s, the scaling variable τ is given by τ =s/s. ˆ (2)

The cross section for the hadronic reaction

a + b → α + anything (3) is given by Z 1 X dτ τ dLij σ(s) = · · [ˆsσˆ (ˆs)] , (4) τ sˆ dτ ij→α {ij} τ0 whereσ ˆij→α is the operative parton-level cross section. The (dimensionless) factor in square brackets is approximately determined by couplings. Many explicit (leading-order) forms ofσ ˆ are given in Refs. [4]. The logarithmic integral typically gives a factor of order unity.

If event rates for signal and backgrounds√ √ are known—by calculation or by measurement—for some point ( s, sˆ), the parton luminosities can be used to estimate the rates at other points, at an accuracy satisfactory for orientation. Because leading-order parton distributions have a simple intuitive interpretation, I have chosen the CTEQ6L1 leading-order parton distributions [5] for the calculations presented in this note. Any of the modern sets of parton distributions will yield similar results for energy-to-energy compar- isons [6].

I present four examples relevant to discovery physics: gluon-gluon interactions, ud¯ interactions, interactions among generic light quarks, and interactions of gluons with light quarks or antiquarks. The parton luminosities 4 Chris Quigg for gluon-gluon interactions are given in Figure1. These are identical for pp andpp ¯ collisions. The parton luminosities for ud¯ interactions are plotted in Figure2. In pp collisions, ud¯ is a valence–sea combination; inpp ¯ collisions, it is valence–valence. The difference is reflected in the excess of√ the Tevatron luminosities in Figure2 over the proton-proton luminosities at s = 2 TeV. The parton luminosities for light-quark–light-quark interactions in pp collisions are displayed in Figure3, as examples of valence–valence interactions leading to final states such as two jets. What is plotted here is the combination (u + d)(1) ⊗ (u + d)(2). (5) Forpp ¯ collisions at the Tevatron, interpret the 2-TeV curve as

(u + d)(p) ⊗ (¯u + d¯)(¯p); (6) these valence–valence interactions are the main source of high-transverse- momentum jets at the Tevatron. The parton luminosities for gluon–light- quark interactions are shown in Figure4. The quantity displayed is the combination (u + d)(1) ⊗ g(2). (7) In pp collisions, the gq luminosity is twice what is shown in Figure4, corresponding to (u + d)(1) ⊗ g(2) + g(1) ⊗ (u + d)(2). Forpp ¯ scattering at the Tevatron, interpret the 2-TeV curve as either (u + d)(p) ⊗ g(¯p) (gq collisions) or g(p) ⊗ (¯u + d¯)(¯p) (gq¯ collisions).

Ratios of parton luminosities are especially useful for addressing what is gained or lost by running at one energy instead of another. Let us consider each of the example cases in turn.

2 Gluon-gluon interactions

Ratios of parton luminosities for gluon-gluon interactions in p±p collisions at specified energies to the gg luminosity at the Tevatron are√ shown in Fig- ure5; ratios to the LHC at design energy in Figure6. At sˆ ≈ 0.4 TeV, characteristic of tt¯ pair production, Figure5 shows that the gg luminosity rises by three orders of magnitude from the 2-TeV Tevatron to the 14-TeV LHC. This rise is the source of the computed increase in the gg → tt¯ cross LHC Physics Potential—2011 Run 5 section from Tevatron to LHC, and is the basis for the (oversimplified) slo- gan, “The Tevatron is a quark collider, the LHC is a gluon collider.” Figure6 shows that the gg → tt¯ yield drops by a bit more than a factor of 6 between ¯ 14 TeV and 7 TeV.√ To first approximation, accumulating a tt sample of specified size at s = 7 TeV will require√ about 6× the integrated luminosity that would have been needed at s = 14 TeV,√ although acceptance cuts should have less effect at the lower energy. At s = 10 TeV, the gg → tt¯ √rate is a factor of 2.3 smaller than at design energy.√ The gg luminosity at sˆ = 0.4 TeV is approximately 1.47× higher at s = 8 TeV than at 7 TeV.

The dominant mechanism for light Higgs-boson production at both the Tevatron and the LHC is gg → top-quark loop → H, so the rates are con- trolled by the gg luminosity. For MH √≈ 120 GeV, the gg luminosity is approximately (20, 25, 38, 70)× larger at s = (7, 8, 10, 14) TeV than at the Tevatron. LHC experiments are likely to rely on the rare γγ decay of a light Higgs boson, for which high integrated luminosities will be required. At somewhat higher Higgs-boson masses, the situation could be more promising for early running. For MH = 175 GeV, a mass at which H → ZZ becomes a signiﬁcant√ decay mode, the gg luminosity is roughly (30, 40, 65, 130)× larger at s = (7, 8, 10, 14) TeV than at the Tevatron. The potential Tevatron sensitivity for gg → H → ZZ, based on the current integrated luminos- −1 ity of 10 fb would be matched√ at the LHC by integrated luminosities of (340, 250, 160, 80) pb−1 at s = (7, 8, 10, 14) TeV. Note that these levels do not correspond to the thresholds needed for discovery (although those could be worked out, given a discovery criterion), but to the point at which the LHC would begin to break new ground, compared to the Tevatron sample now in hand. The parton-luminosity advantage of 8-TeV over 7-TeV running is 1.3 for 120-GeV gg collisions, 1.34 for√ 175-GeV gg collisions, and 1.47 for 400-GeV gg collisions (see Figure7). By sˆ ≈ 4 TeV, the multiplier reaches an order of magnitude (see Figure8).

3 ud¯ interactions

Ratios of parton luminosities for ud¯interactions in pp collisions at speciﬁed energies to the ud¯ luminosity inpp ¯ collisions at the Tevatron are plotted in Figure9. Ratios to the LHC at design energy are shown in Figure 10. These 6 Chris Quigg ratios of luminosities apply directly to the production of W bosons and to the search for new W 0 bosons. They are also indicative of the behavior of uu¯ and dd¯luminosities, which enter the production of Z, Z0, and W +W − or ZZ pairs that are backgrounds to Higgs-boson searches for MH & 140 GeV. For the + case of W production,√ Figure9 shows that the rates will be higher by factors of (4.4, 5, 6.4, 9) at s = (7, 8, 10, 14) TeV, compared to the Tevatron rate. At an invariant mass of 175 GeV, the curves in Figure9 show that the rate for the background processes qq¯ → VV (V = W, Z) grows less rapidly than the rate for the signal process gg → H discussed in the previous paragraph. The√ enhancements over the Tevatron are by factors of (4.8, 5.6, 7.3, 10.7) at s = (7, 8, 10, 14) TeV.

0 For a W search at MW 0 √= 1 TeV, the production rates are larger by factors of (134, 190, 308, 580) at s = (7, 8, 10, 14) TeV, so the Tevatron’s 10 fb−1 sensitivity would be matched at integrated luminosities of approximately (75, 53, 33, 17) pb−1, before taking into account relative detector acceptances. At still higher masses, the penalty for LHC running below design energy is correspondingly greater. At MW 0 = 2 TeV,√ the rates are diminished by factors of approximately 2.95, 7.8, and 16 at s = (10, 8, 7) TeV. For high- mass searches, one must refer back to the parton luminosities themselves (Figure2) to check whether the absolute rates give adequate sensitivity.

¯ ¯ The qq¯ contribution to tt production√ will also track the ratios of ud luminosities. In the range of interest, sˆ ≈ 0.4 TeV, the rate is enhanced √over the Tevatron (¯pp collisions!) rate by factors of roughly (7, 8, 11, 18) at s = (7, 8, 10, 14) TeV, far smaller than the enhancements we noted above for the gg → tt¯ rates. The behavior of the ud¯ parton luminosities also deter- mines how rates for H(W ±,Z) associated production and for pair production of new colored particles (e.g., superpartners) scale under diﬀerent operating conditions. Figure 11 summarizes the ud¯-luminosity advantage of 8-TeV over 7-TeV running. For the cases mentioned√ in the preceding discussion, the 8- TeV ud¯-luminosity multipliers are sˆ = 0.08 TeV: 1.15; 0.175 TeV: 1.18; 0√.4 TeV: 1.22; 1 TeV: 1.41; and 2 TeV: 2.05. By 4 TeV, the advantage of s = 8 TeV over 7 TeV reaches an order of magnitude (see Figure 12). LHC Physics Potential—2011 Run 7

4 Light-quark–light-quark interactions

Ratios of parton luminosities for generic light-quark–light-quark interactions in pp collisions at speciﬁed energies to the corresponding light-quark– light-antiquark interactions inpp ¯ collisions at the Tevatron are displayed in Figure 13. Ratios of the same luminosities to the LHC at design energy appear in Figure 14. Such valence–valence interactions govern the production of hadron jets√ at very large values of p⊥. Figure 13 reveals that for jet production√ at sˆ ≈ 1 TeV, qq → two jets will be enhanced at LHC energies s = (7, 8, 10, 14) TeV by factors of (160, 195, 266, 400) over the rate for qq¯ → two jets at the Tevatron. At scales beyond those accessible at the Tevatron,√ a relevant question is how much rates√ are diminished in running√ below s = 14 TeV (see Figure 14). For sˆ = 2 TeV, the rates at s = (7, 8, 10) TeV are (0√.17, 0.27, 0.51)× those at design energy. The corresponding multipliers at sˆ = 4 TeV are (0.007, 0.031, 0.18). Figure 15 exhibits the qq-luminosity advantage of 8-TeV running√ with respect to 7-TeV running. The 8-TeV luminosity multipliers are sˆ = 1 TeV: 1.23; 2 TeV: 1.59;√ and 4 TeV: 4.54. For this valence-valence combination, the advantage of√ s = 8 TeV over 7 TeV reaches an order of magnitude at approximately sˆ = 5 TeV (see Figure 16).

5 Gluon–light-quark interactions

Collisions of gluons with light (mostly valence) quarks are important com- ponents of prompt-photon production and single–top-quark production, as √well as jet production at intermediate values of transverse momentum. At sˆ = 300 GeV, typical for the Tevatron, gq parton√ luminosities are higher than at the Tevatron by factors of (21, 27, 39, 67)√ for s = (7, 8, 10, 14) TeV, as shown√ in Figure 17. At the higher scale of sˆ = 1 TeV. the gq luminosities at s = (7, 8, 10) TeV are smaller by factors of (6.9, 4.4, 2.3) compared to the 14-TeV values (see Figure√ 18). The advantage of 8-TeV√ over 7-TeV running is a factor of 1.27 at sˆ = 0.3 TeV and 1.53 at √sˆ = 1 TeV (see Figure 19). Figure 20 shows that the relative√ advantage of s = 8 TeV over 7 TeV reaches an order of magnitude at sˆ ≈ 4.4 TeV. 8 Chris Quigg

6 Parton luminosity contours

√ Contour√ plots showing at each hadron c.m. energy s the parton-parton energy sˆ that corresponds to a particular value of parton luminosity (τ/sˆ)dL/dτ provide another tool for judging the eﬀects of changes in beam energy or proton-proton luminosity. Plots for the four varieties of parton- parton collisions considered in this note are given in Figures 21–24, for proton-proton energies between 2 and 14 TeV. The advantage of 2-TeVpp ¯ collisions over 2-TeV pp collisions for ud¯ interactions (at the same hadron luminosity) is indicated by the Tevatron points in Figure 22. The contour plots summarize a great deal of information, and will reward detailed study. As for the parton luminosity and ratio plots, contemplating the contour plots will be particularly informative to the user who brings a thorough understanding of signals and backgrounds at one or more beam energies.

7 Final remarks

Operational considerations will determine the beam energy for the 2011- 2012 run of the Large Hadron Collider: safe, consistent operation that leads to high integrated luminosity must be the goal. Should it be practical to increase the beam energy from 3.5 TeV to 4 TeV, the benefits to sensitivity are not inconsiderable. The benefits vary for different signals and backgrounds, so considering a representative sample of parton luminosities provides an efficient orientation. √ Over the range of parton-parton collision√ energies from sˆ = 0.1 to 1 TeV, the parton-luminosity enhancement for s = 8 TeV compared with 7 TeV ranges from about 15% to 80%, as recapitulated in Table1. The improve- ment is greatest for gluon-gluon collisions and least for quark-quark√ collisions. At higher scales, the effect is more pronounced: at sˆ = 4 TeV, the 8 TeV : 7 TeV multiplier is an order of magnitude for gg and ud¯ interactions, 4.5 for qq collisions, and 6.9 for gq collisions. In the end, the product of hadron luminosity and parton luminosity is the figure of merit that in- fluences physics performance. The pp luminosity is likely to be higher (for LHC Physics Potential—2011 Run 9

ﬁxed beam currents) at the higher beam energy. This would bring a double bonus.

The true promise of the LHC will be realized in high-luminosity running −1 near√ the design energy. For the immediate future, accumulating several fb at s = 8 TeV would begin a thorough exploration of the TeV scale and the origins of electroweak symmetry breaking. √ √ Table 1: Ratio of s = 8 TeV to s = 7 TeV parton luminosities. √ √ √ Partons sˆ = 0.1 TeV sˆ = 1 TeV sˆ = 4 TeV gg 1.28 1.81 9.72 ud¯ 1.16 1.41 9.60 qq 1.14 1.23 4.54 gq 1.20 1.53 6.87

Fermilab is operated by the Fermi Research Alliance under contract no. DE-AC02- 07CH11359 with the U.S. Department of Energy. I am grateful to Ignatios Antoniadis and the CERN Theory Group for warm hospitality.

References

[1] C. Quigg, “LHC Physics Potential vs. Energy,” arXiv:0908.3660 [hep-ph]. FERMILAB-FN-0839-T. [2] “LHC End-of-Year Jamboree, December 17, 2010,” indico.cern.ch/conferenceDisplay.py?confId=113139. [3] S. Alekhin, J. Blumlein, P. Jimenez-Delgado, S. Moch, and E. Reya, “NNLO Benchmarks for Gauge and Higgs Boson Production at TeV Hadron Colliders,” arXiv:1011.6259 [hep-ph]. [4] E. Eichten, I. Hinchliﬀe, K. D. Lane, and C. Quigg, Rev. Mod. Phys. 56, 579–707 (1984). Addendum-ibid. 58, 1065 (1986). See also R. K. Ellis, W. J. Stirling, and B. R. Webber, QCD & Collider Physics (Cambridge University Press, Cambridge, 1996) §7.2; R. K. Ellis, Scottish Universities Summer School in Physics 2009; and plots on the Martin-Stirling-Thorne-Watt parton distribution functions web site. [5] CTEQ Collaboration, J. Pumplin et al., JHEP 07, 012 (2002) [arXiv:hep-ph/0201195]. [6] W. J. Stirling, “Ratios of LHC parton luminosities,” www.hep.phy.cam.ac.uk/~wjs/plots/lumi_LHC_789.eps. 10 Chris Quigg

CTEQ6L1: gg 106 105 104 103 102 101 0 0.9 TeV 10 2 TeV 10-1 4 TeV 6 TeV 10-2 7 TeV 8 TeV Parton Luminosity [nb] -3 10 10 TeV 10-4 14 TeV 10-5 10-6 10-2 10-1 100 101 [TeV]

Figure 1: Parton luminosity (τ/sˆ)dL/dτ for gg interactions. LHC Physics Potential—2011 Run 11

— CTEQ6L1: ud 106 105 104 103 102 101 0.9 TeV 2 TeV 0 10 Tevatron -1 4 TeV 10 6 TeV 10-2 7 TeV 8 TeV Parton Luminosity [nb] -3 10 10 TeV 10-4 14 TeV 10-5 10-6 10-2 10-1 100 101 [TeV]

Figure 2: Parton luminosity (τ/sˆ)dL/dτ for ud¯ interactions. 12 Chris Quigg

CTEQ6L1: qq 106 105 104 103 102 101 0.9 TeV 0 2 TeV 10 4 TeV 10-1 6 TeV 7 TeV 10-2 8 TeV 10 TeV Parton Luminosity [nb] -3 10 14 TeV 10-4 10-5 10-6 10-2 10-1 100 101 [TeV]

Figure 3: Parton luminosity (τ/sˆ)dL/dτ for qq interactions. See the text surrounding (5) and (6) for deﬁnitions. LHC Physics Potential—2011 Run 13

CTEQ6L1: gq 106 105 104 103 102 101 0.9 TeV 0 2 TeV 10 4 TeV 10-1 6 TeV 7 TeV 10-2 8 TeV 10 TeV Parton Luminosity [nb] -3 10 14 TeV 10-4 10-5 10-6 10-2 10-1 100 101 [TeV]

Figure 4: Parton luminosity (τ/sˆ)dL/dτ for gq interactions. See the text surrounding (7) for deﬁnitions. 14 Chris Quigg

CTEQ6L1: gg 103

102

101 evatron T R.9 100 R4 R6 Ratio to R7 R8 10-1 R10 R14

10-2 10-2 2*10-2 10-1 2*10-1 100 [TeV]

Figure 5: Comparison of parton luminosity for gg interactions at speciﬁed energies with luminosity at 2 TeV. LHC Physics Potential—2011 Run 15

CTEQ6L1: gg 100

10-1 eV T R.9 R2 R4 R6 R7

Ratio to 14 -2 10 R8 R10

10-3 10-2 10-1 100 101 [TeV]

Figure 6: Comparison of parton luminosity for gg interactions at speciﬁed energies with luminosity at 14 TeV. 16 Chris Quigg

CTEQ6L1: gg Parton Luminosity 2.0 1.9 1.8 1.7 1.6 1.5 1.4

[8 TeV] / [7 TeV] / [7 TeV] [8 1.3 1.2 1.1 1.0 10-2 10-1 100 101 [TeV]

√Figure 7: Ratio of parton luminosity for gg interactions in pp collisions at s = 8 TeV to luminosity at 7 TeV. LHC Physics Potential—2011 Run 17

CTEQ6L1: gg Parton Luminosity 10

8 7 6 5

[8 TeV] / [7 TeV] / [7 TeV] [8 2

1 10-2 10-1 100 101 [TeV]

√Figure 8: Ratio of parton luminosity for gg interactions in pp collisions at s = 8 TeV to luminosity at 7 TeV (logarithmic scale). 18 Chris Quigg

— CTEQ6L1: ud 103

102

1 10 R0.9 R2 R4 100 R6 R7

Ratio to Tevatron Ratio to R8 R10 10-1 R14

10-2 10-2 2*10-2 10-1 2*10-1 100 [TeV]

Figure 9: Comparison of parton luminosity for ud¯interactions in pp collisions at speciﬁed energies with luminosity inpp ¯ collisions at 2 TeV. LHC Physics Potential—2011 Run 19

— CTEQ6L1: ud 100

10-1

R0.9 R2 RTev R4 Ratio to 14 TeV Ratio to 14 10-2 R6 R7 R8 R10

10-3 10-2 10-1 100 101 [TeV]

Figure 10: Comparison of parton luminosity for ud¯ interactions at speciﬁed energies with luminosity at 14 TeV. 20 Chris Quigg

– CTEQ6L1: ud Parton Luminosity 2.0 1.9 1.8 1.7 1.6 1.5 1.4

[8 TeV] / [7 TeV] / [7 TeV] [8 1.3 1.2 1.1 1.0 10-2 10-1 100 101 [TeV]

¯ √Figure 11: Ratio of parton luminosity for ud interactions in pp collisions at s = 8 TeV to luminosity at 7 TeV. LHC Physics Potential—2011 Run 21

– CTEQ6L1: ud Parton Luminosity 10

8 7 6 5

[8 TeV] / [7 TeV] / [7 TeV] [8 2

1 10-2 10-1 100 101 [TeV]

¯ √Figure 12: Ratio of parton luminosity for ud interactions in pp collisions at s = 8 TeV to luminosity at 7 TeV (logarithmic scale). 22 Chris Quigg

CTEQ6L1: qq 103

102

eV 1 T 10 R0.9 R4 100 R6

Ratio to 2 R7 R8 R10 10-1 R14

10-2 10-2 2*10-2 10-1 2*10-1 100 [TeV]

Figure 13: Comparison of parton luminosity for qq interactions at speciﬁed energies with luminosity at 2 TeV. LHC Physics Potential—2011 Run 23

CTEQ6L1: qq 100

10-1 eV T R0.9 R2 R4 R6 Ratio to 14 10-2 R7 R8 R10

10-3 10-2 10-1 100 101 [TeV]

Figure 14: Comparison of parton luminosity for qq interactions at speciﬁed energies with luminosity at 14 TeV. 24 Chris Quigg

CTEQ6L1: qq Parton Luminosity 2.0 1.9 1.8 1.7 eV] T 1.6 1.5

eV] / [7 1.4 T

[8 1.3 1.2 1.1 1.0 10-2 10-1 100 101 [TeV]

√Figure 15: Ratio of parton luminosity for qq interactions in pp collisions at s = 8 TeV to luminosity at 7 TeV. LHC Physics Potential—2011 Run 25

CTEQ6L1: qq Parton Luminosity 10 8 7 6 5 eV]

T 4

3 eV] / [7 T

[8 2

1 10-2 10-1 100 101 [TeV]

√Figure 16: Ratio of parton luminosity for qq interactions in pp collisions at s = 8 TeV to luminosity at 7 TeV (logarithmic scale). 26 Chris Quigg

CTEQ6L1: gq 103

102

eV 1 T 10 R0.9 R4 100 R6

Ratio to 2 R7 R8 R10 10-1 R14

10-2 10-2 2*10-2 10-1 2*10-1 100 [TeV]

Figure 17: Comparison of parton luminosity for gq interactions at speciﬁed energies with luminosity at 2 TeV. LHC Physics Potential—2011 Run 27

CTEQ6L1: gq 100

10-1

R0.9 R2 R4 R6 Ratio to 14 TeV Ratio to 14 10-2 R7 R8 R10

10-3 10-2 10-1 100 101 [TeV]

Figure 18: Comparison of parton luminosity for gq interactions at speciﬁed energies with luminosity at 14 TeV. 28 Chris Quigg

CTEQ6L1: gq Parton Luminosity 2.0 1.9 1.8 1.7 1.6 1.5 1.4

[8 TeV] / [7 TeV] / [7 TeV] [8 1.3 1.2 1.1 1.0 10-2 10-1 100 101 [TeV]

Figure√ 19: Ratio of parton luminosity for gq interactions in pp collisions at s = 8 TeV to luminosity at 7 TeV. LHC Physics Potential—2011 Run 29

CTEQ6L1: gq Parton Luminosity 10

8 7 6 5

[8 TeV] / [7 TeV] / [7 TeV] [8 2

1 10-2 10-1 100 101 [TeV]

Figure√ 20: Ratio of parton luminosity for gq interactions in pp collisions at s = 8 TeV to luminosity at 7 TeV (logarithmic scale). 30 Chris Quigg

CTEQ6L1: gg 10

5 4 3

2 0.1 pb 1 pb 10 pb [TeV] 1 100 pb 1 nb 0.5 10 nb 0.4 0.3 0.2

0.1 2 3 4 5 6 7 8 10 14 [TeV]

Figure 21: Contours of parton luminosity for gg interactions in p±p collisions. LHC Physics Potential—2011 Run 31

— CTEQ6L1: ud 10

5 4 3 2 0.1 pb 1 pb 10 pb [TeV] 1 100 pb 1 nb 0.5 10 nb 0.4 0.3 0.2

0.1 2 3 4 5 6 7 8 10 14 [TeV]

¯ Figure 22:√ Contours of parton luminosity for ud interactions in pp collisions. Values of sˆ corresponding to the stated values forpp ¯ collisions at the Teva- tron are shown as points at E = 2 TeV. 32 Chris Quigg

CTEQ6L1: qq 10

5 4 3 0.1 pb 2 1 pb 10 pb 100 pb

[TeV] 1 1 nb 10 nb 0.5 0.4 0.3 0.2

0.1 2 3 4 5 6 7 8 10 14 [TeV]

Figure 23: Contours of parton luminosity for qq interactions in pp collisions or qq¯ interactions inpp ¯ collisions. LHC Physics Potential—2011 Run 33

CTEQ6L1: gq 10

5 4 3 0.1 pb 2 1 pb 10 pb eV] 100 pb

[ T 1 1 nb 10 nb 0.5 0.4 0.3 0.2

0.1 2 3 4 5 6 7 8 10 14 [TeV]

Figure 24: Contours of parton luminosity for gq interactions (×1/2) in pp collisions and either gq or gq¯ interactions inpp ¯ collisions.